S_N1 vs. S_N2 - Nucleophilic Substitution of Alkyl Halides

Background: McM Chapter 11 to section 11.10. An alkyl halide, R-X, serves as the reactant or "substrate" in almost all nucleophilic substitution reactions. These include a number of useful preparative reactions leading to a wide variety of products. The mechanisms of nucleophilic substitution have been studied extensively to account for the effects of solvent, structure of the halide, nature of the leaving group, and other factors.

The S_N2 process is a displacement, with the nucleophile, Nu:^- approaching from the side opposite the C-Y bond as the Y^- anion leaves. In McM, especially Fig 11.6, the substrate is depicted as a tetrahedral carbon atom bonded to the leaving group, Br (red) while the nucleophile attack is shown by the arrow. In this mechanism the carbon atom making and breaking bonds invariably undergoes inversion. This Figure also shows how this mechanism is favored if the substrate is open to unhindered attack by nucleophiles, that is, if the substrate is a methyl halide (and progressively less ideal if the substrate is 1^o then 2^o then 3^o). The S_N2 mechanism is also favored if the nucleophile is reactive; iodide is one such powerful nucleophile.

Solvents and structural features favoring the S_N1 mechanism are based an entirely distinct set of criteria because its rate limiting step is different. In this mechanism, (see 11.9) the C-halogen bond breaks first, and the resulting carbocation reacts with a nucleophilic solvent to form a new bond. The focus of the mechanism is on the first step, the formation of a carbocation and a halide ion; for this reason the S_N1 reaction is often called solvolysis. Examining the structural effect of the substrate we note that more substituted carbocations are more stable. The process leading to the more substituted ion will be faster. Note that this effect is in the opposite direction as that for the S_N2 reaction. For the solvent effect, we envision the gradual stretching of the C-X bond and formation of C⁺ and X^- ions. Solvents that stabilize these ions will also expedite the process leading to their formation.

In the experiments below you will use solvent-nucleophile combinations that will enforce either the S_N1 or the S_N2 reaction.

The Solvent-Nucleophile Combination for the S_N1 Reaction: Water would be the ideal solvent because its high dielectric polarization property (Table 11.3) best stabilizes the ions formed and therefore reduces the energy needed to form them. In addition, water is protic; it has hydrogen bonding capability. This property allows specific stabilization of the halide ion as it is being formed (diagram McM p. 399). Unfortunately pure water cannot initially dissolve alkyl halides. Therefore ethanol (less polar but also protic) is added to the water to make the solvent combination as polar as possible, yet capable of dissolving the substrates to be studied. To make a test practical, however we must be able to see some change, and in the ethanol we also dissolve a silver salt. Ag⁺ ions will form a precipitate with the halide ions as they free themselves from the substrate. Ag⁺ cannot be introduced alone, but as a salt. The anion chosen to balance the Ag⁺ cannot be nucleophilic, or the S_N2 reaction may compete; instead the nitrate ion, a very weak nucleophile is used. Thus "1% ethanolic silver nitrate" is the solvent-nucleophile combination that best favors the S_N1 mechanism and least favors the S_N2 mechanism.

R-X in 95% ethanol -----> R⁺ + X^- (ionization step - rate limiting)

then X^- + AgNO₃ -----> Ag-X(insoluble in ethanol) + NO₃^-

The Solvent-Nucleophile Combination for the S_N2 Reaction: This reaction is observed by displacement of chloride or bromide by iodide ion in acetone solution. As noted above, iodide is the powerful nucleophile necessary for S_N2 displacement (Table 11.1). The solvent, acetone, is chosen because its low dielectric polarization, 21 (compare Table 11.3) discourages S_N1 solvolysis. Just as important, acetone is aprotic. Its lack of hydrogen bonding actually promotes the S_N2 mechanism by preventing the iodide ion from being solvated (p. 399) before the reaction. This effect is depicted in Figure 11.7 part d). Sodium iodide is very soluble in acetone, but sodium chloride and sodium bromide have very low solubilities (this fact will be useful if you need to identify an alkyl halide in a future lab.) The course of the reactions can therefore be seen by the formation of a crystalline deposit of NaCl or NaBr. Question: why aren't alkyl iodides tested?

R-Halide + NaI in acetone ------> R-I + Na-Halide (insoluble in acetone)

The laboratory session is divided into three parts and the work is carried out students working in pairs.

Part A, Structural Effects on S_N1 and S_N2 Reactivity.  The reactivities of various alkyl halides will be compared under S_N1 and also under S_N2 conditions.

Part B, Solvent Effects on S_N1 (solvolysis) Reactivity.  In this and the following section the S_N1 mechanism is enforced by the use of t-butyl chloride in all the tests. The solvents ethanol, water, methanol and acetone will be compared for their ability to ionize R-Halide substrates. Tabulation of the times needed to reach a standard point of ion formation will allow comparison of the effectiveness of these solvents in this step - the rate limiting step of the S_N1 reaction.

The most suitable method for comparing solvolysis rates is based on the fact that a strong acid is liberated in the reaction:

t-Bu-Cl + ROH -----> t-Bu-OR + HCl (rate constant: k)

To determine when the reaction has proceeded to a certain extent, enough base is added to the reaction mixture to neutralize a small fraction of the acid produced. The solution becomes acidic after that fraction of the t-butyl chloride has reacted, and the change in pH is detected with phenolphthalein. The time required for neutralization is inversely proportional to the rate constant, k, of the reaction shown in the above equation.

Part C, Temperature Effect on the Rate of a Solvolysis (S_N1) Reaction. You will repeat one of the reactions you carried out in Part B at various temperatures to determine its energy of activation, deltaG^± (also known as E_act - McM, p. 174).

The rate of a reaction increases with increasing temperature because of the greater kinetic energy of the reacting molecules. The effect of temperature on the rate constant, k, of a reaction is expressed by the following equation where deltaG^± is the activation energy, T is the temperature in ^oK, P is the probability factor, Z is the collision frequency, and R is the gas constant, 8.31Joule/mole ^oK:

k = PZ·exp(-deltaG^±/RT) = PZ·e^-deltaG±.^/RT

The activation energy can be obtained if the rate constant is known at two or more temperatures. Using the logarithmic form of the above equation, it is seen that a plot of log t vs. 1/T gives a straight line with slope equal to deltaG^±/2.3R. To show this, the log of both sides is taken:

log k = log PZ - deltaG^±/2.3RT = log PZ - (deltaG^±/2.3R)[1/T].

The rate of the reaction, k is inversely proportional to the time, t, necessary for a color change for a standard reaction:

k = const/t;

taking logs of both sides of the equation,

log k = log const - log t.

Equating the two expressions for log k and then rearranging to isolate log t,

log t = log const - log PZ + (deltaG^±/2.3R)[1/T].

And we have an equation of the form y = mx + b, where

y = log t; and b = log const - log PZ; and x = [1/T]

and the slope, m, equals: deltaG^±/2.3R

Therefore a plot of log t values vs. 1/T should give a straight line with slope of deltaG^±/2.3R from which the value of deltaG^± can be obtained.

The effect of temperature on the rate of solvolysis of tert-butyl chloride can be studied using the procedure and solvent mixtures of Part B at different temperatures. To obtain conveniently measurable rates, a solvent mixture should be used which gives an end point (color change) at about eight minutes in Part B.

Procedures:

Part A. Structural Effects on S_N1 and S_N2 Reactivity.
   

Label two series of five clean, dry 13x100 mm test tubes with the symbols: n-Bu-Cl, n-Bu-Br, sec-Bu-Cl, t-Bu-Cl, and CR-Cl. In each series of tubes, place 0.2 mL of the following halides: n-butyl chloride, n-butyl bromide, sec-butyl chloride, tert-butyl chloride, crotyl chloride [CH₃CH=CHCH₂Cl]. Obtain 15 mL of 15% NaI-acetone solution and 15 mL of 1% ethanolic AgNO₃ solution from the side shelf.

Set up a table to organize the times taken by each substrate and notes of the changes you observe. Using a pipette add 2 mL of the NaI solution to the tube labeled n-Bu-Cl, note the time and swirl the tube to thoroughly mix the reagents. After two to three minutes, add 2 mL of NaI solution to the next tube and again note its time and changes. Continue at two- to three-minute intervals with the remaining tubes. After each addition, watch for any rapid reaction and then inspect the other tubes for signs of a precipitate. Allow all the tubes to stand, observing them periodically while the next series is run.

Arrange the second series of tubes, and in the same way add 2 mL portions of the AgNO₃ solution to each tube at two-minute intervals. Again, watch closely for any rapid changes and then observe the others periodically. If possible, note the time both for the first appreciable turbidity and also for a definite precipitate. If any tubes in the NaI series are still clear at this point, place the tubes in a water bath at 50 ^oC; note any changes that occur. Rank the substrates 1 (fastest) to 5 for their reactivities in the S_N1 reaction and again in the S_N2 reaction.

Repeat the experiments as necessary until you are confident of the results. Does the order of reactivity of substrates differ from the order predicted in McM? If so, compare your results with other groups and note differences in your findings. In any case, when you interpret data, interpret it with your data, not expected data. When you have completed these test tube reactions, pour the contents of all of the test tubes into the drain.

Part B, Solvent Effects of S_N1 (Solvolysis) Reactivity.
   

The class is to fill in the blanks for Table 2, below. To do this, each group (of two students) will fill in times (each averaged from two runs) for two different solvent mixtures. The assignments will be organized on the blackboard.    

Each group reserves two different solvent mixtures by initialing through "sec"s on the blackboard for two different solvent mixtures. Run each solvent mixture, details below, and report the results on the blackboard. When all numbers are reported and averaged, copy all the data into your own table.

Table 2: Times for the S_N1 Reaction of tert-Butyl Chloride in Various Solvent Mixtures at 30 ^oC:

Prepare two clean dry 13x100 mm test tubes for each solvent mixture. Using a graduated pipet to measure the volumes, prepare 2.0 mL of the appropriate solvent mixture in each tube according to the table above.

Run this test in duplicate; if the two times are significantly different, repeat the experiment until the data are consistent. To each test tube add three drops (only) of 0.5 M NaOH solution containing phenolphthalein indicator. Cork the tubes and place them in a bath containing a thermometer and water at 30±1 ^oC. A Styrofoam cup placed in an empty beaker for stability makes a convenient insulated container for the bath. Wait a minute in the bath to bring the solvent to temperature. To each test tube add three drops (only) of tert-butyl chloride from a Pasteur pipette. Note the time of addition, shake or swirl the test tubes to mix the solutions, and replace them in the bath. Add a few mL of hot water as needed to maintain the temperature at 30±1 ^oC. Record the time required for the pink (basic) color to disappear in each solvent mixture; express the time in seconds - thus 3 min 40 sec would be recorded as 220 sec. Enter your average value in the appropriate space on the blackboard. Repeat the procedure for the other solvent mixture you are assigned.

Part C, Temperature Effect on the Rate of a Solvolysis (S_N1) Reaction.

From your results in Part B select the solvent mixture you used which is closest to eight minutes. Prepare two 2-mL mixtures of this solvent composition and add three drops of NaOH indicator solution as in part B. (Duplicate samples should be run as before.)

Adjust the temperature of the water bath to 20±1 ^oC, insert both tubes, and allow one minute for temperature equilibration. Note the time, add three drops of tert-butyl chloride with a Pasteur pipette to each tube, mix, and measure the time required for the color to disappear.

Repeat the procedure twice again after adjusting the bath temperature to 40±1 ^oC. Organize your data by completing the following table in your notebook:

Make a plot of the log t_avg values (vertical axis) versus the corresponding 1/T values (horizontal axis). The high and low values on each axis should be spread out over most of an entire notebook page. Neither axis should start at 0.0. Plot the three points and then draw a single, straight line that comes closest these points. The use of Excel is encouraged. Determine the slope (which will be in units of ^oK) without using the origin as a data point. Calculate the activation energy for the solvolysis of tert-butyl chloride in the solvent used by multiplying the slope value by 2.3.R. Show your calculations.

Questions: Answer in the Conclusion.

1. Give a drawing of the transition state of the S_N2 reaction and point out how changes in the substituents should account for the relative reactivities in Part A for the alkyl halides with NaI-acetone. Did the order of reactivity you observed agree with this explanation?

2. Similarly, sue a drawing to explain the relative reactivities of the alkyl halide substituents with AgNO₃-ethanol. Again report if your observations agreed with this expalanation.

3. Indicate how the data obtained by your class in Part B, allows the following solvents to be arranged in order of increasing rate in the S_N1 reaction: water, acetone, methanol, and ethanol. Does this order parallel the dielectric polarization in McM Table 11.3 (acetone's value is 21)? Based on your findings, would ethanol have more or less solvent ionizing power than 1-propanol (CH₃CH₂CH₂OH)?

4. With the procedure used in Part B or C, would the color change occur sooner, later, or at the same time if (a) twice as much t-butyl chloride were used (six drops); (b) twice as much NaOH-phenolphthalein solution were used?

5. Draw a sketch of the reaction coordinate diagram for the solvolysis of t-butyl chloride, labeling the maxima and minima with appropriate structures, and indicating the activation energy measured in Part C.

References:

"Mayo et al." Mayo, D.W., Pike, R.M., Butcher, S.S. and Trumper, P.K. Microscale Techniques for the Organic Laboratory; Wiley: New York, 1991

"McM": McMurry, J. Organic Chemistry, 4th ed., Brooks/Cole Publishing Company, Pacific Grove, CA. 1996

Moore, J.A, and Dalrymple, D.L., Experimental Methods in Organic Chemistry, 2nd Ed.; Saunders: Philadelphia, 1976 p. 139.

Rev. December, 1999